Known 17-digit prime factors of Googolplex + 10

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  2. Number Theory
  3. Known 17-digit prime factors of Googolplex + 10

This is a list of known 17-digit prime factors of googolplex + 10, i.e., 1010^100 + 10.

These numbers have the form 1 + 2k ∏i piei, where pi is a prime factor of 10100 − 1 and ei is zero or one.

The list of prime factors of 10100 − 1 is: 3, 3, 11, 41, 101, 251, 271, 3541, 5051, 9091, 21401, 25601, 27961, 60101, 7019801, 18 2521213001, 1410 3673319201, 7887 5943472201 and 168058 8011350901.

In the list you can see the prime factors, their discoverer and their corresponding value of k.

  1. 1002239 0619214807 (David Broadhurst, k=7)
  2. 1015937 9458656133 (David Broadhurst, k=2)
  3. 1027248 0001027249 (David Broadhurst, k=8)
  4. 1028760 7490438533 (David Broadhurst, k=2)
  5. 1039272 7857621133 (Phil Carmody, k=662)
  6. 1070428 2458954173 (David Broadhurst, k=62)
  7. 1074448 2019127573 (Patrick Demichel, k=526586)
  8. 1076825 2274445931 (Phil Carmody, k=155)
  9. 1081818 0001081819 (David Broadhurst, k=1)
  10. 1115888 9885847317 (David Broadhurst, k=38)
  11. 1116223 4906162539 (Phil Carmody, k=373)
  12. 1118537 8744268917 (David Broadhurst, k=2)
  13. 1121036 4858601099 (David Broadhurst, k=1)
  14. 1122557 1136632733 (David Broadhurst, k=2)
  15. 1156754 1181891441 (David Broadhurst, k=40)
  16. 1162115 1929957197 (Phil Carmody, k=926)
  17. 1163353 7074257739 (David Broadhurst, k=1)
  18. 1195326 3552040207 (Norm Dresner, k=13017)
  19. 1206091 2947796127 (Patrick Demichel, k=76807)
  20. 1212239 9998787761 (Phil Carmody, k=120)
  21. 1219741 4852704891 (David Broadhurst, k=5)
  22. 1224378 0001224379 (David Broadhurst, k=1)
  23. 1256689 7372687407 (Patrick Demichel, k=563521)
  24. 1266420 3123932681 (Phil Carmody, k=940)
  25. 1269918 7530149077 (Phil Carmody, k=466)
  26. 1290088 7922082169 (David Broadhurst, k=4)
  27. 1291530 4593214717 (Patrick Demichel, k=92022)
  28. 1298048 3897439103 (Patrick Demichel, k=53437)
  29. 1322222 0001322223 (David Broadhurst, k=1)
  30. 1342999 2976349447 (Phil Carmody, k=343)
  31. 1348204 8095800093 (Phil Carmody, k=1814)
  32. 1369243 1734154053 (David Broadhurst, k=2)
  33. 1371244 6933159411 (David Broadhurst, k=45)
  34. 1377594 9316495081 (Phil Carmody, k=2860)
  35. 1429216 6032865997 (David Broadhurst, k=38)
  36. 1461400 7526213877 (David Broadhurst, k=2)
  37. 1466233 7835439409 (Phil Carmody, k=424)
  38. 1480667 1150583423 (David Broadhurst, k=9)
  39. 1505799 9075215611 (David Broadhurst, k=45)
  40. 1514098 4450388809 (Phil Carmody, k=4244)
  41. 1527708 6401245411 (Patrick Demichel, k=1352435)
  42. 1528427 2413795727 (Phil Carmody, k=281)
  43. 1541990 0809534453 (Patrick Demichel, k=48202)
  44. 1559177 8136424019 (Paul Leyland, k=38561)
  45. 1604809 4110458499 (David Broadhurst, k=11)
  46. 1616964 4442827481 (Phil Carmody, k=340)
  47. 1684342 5601771693 (Patrick Demichel, k=155694)
  48. 1686146 3013165007 (Patrick Demichel, k=114391)
  49. 1732094 3002304533 (David Broadhurst, k=2)
  50. 1745275 6764563077 (David Broadhurst, k=2)
  51. 1757665 8697429327 (David Broadhurst, k=1)
  52. 1762613 0774072419 (David Broadhurst, k=13)
  53. 1795262 5696584811 (David Broadhurst, k=35)
  54. 1818405 1837609081 (Patrick Demichel, k=1609780)
  55. 1908644 2950120877 (David Broadhurst, k=2)
  56. 1934603 8358331103 (Phil Carmody, k=1727)
  57. 1938356 9964714979 (David Broadhurst, k=11)
  58. 1959856 5628205183 (David Broadhurst, k=1)
  59. 1968501 5548699531 (David Broadhurst, k=5)
  60. 1976667 2986953223 (Patrick Demichel, k=9579)
  61. 1980148 6338613813 (Phil Carmody, k=434)
  62. 1983571 4608865893 (Phil Carmody, k=1454)
  63. 2003056 7852451733 (David Broadhurst, k=2)
  64. 2036124 0140678623 (David Broadhurst, k=29)
  65. 2037618 0002037619 (David Broadhurst, k=1)
  66. 2116685 9643265213 (David Broadhurst, k=2)
  67. 2155658 7423787967 (David Broadhurst, k=23)
  68. 2166364 4467133659 (John Gamble, k=15983)
  69. 2181052 9071956813 (Patrick Demichel, k=548806)
  70. 2230043 2542731771 (David Broadhurst, k=35)
  71. 2268816 7826852893 (John Gamble, k=17654)
  72. 2275342 0942871173 (David Broadhurst, k=2)
  73. 2278703 5838020213 (David Broadhurst, k=22)
  74. 2291941 8318666383 (David Broadhurst, k=1)
  75. 2293131 9184698739 (Patrick Demichel, k=5563)
  76. 2303252 2277061091 (Patrick Demichel, k=108265)
  77. 2304639 3814833533 (David Broadhurst, k=26)
  78. 2307597 2787474847 (Phil Carmody, k=197)
  79. 2345157 7430191087 (David Broadhurst, k=61)
  80. 2362201 8658439437 (David Broadhurst, k=2)
  81. 2401256 7876386623 (Phil Carmody, k=1417)
  82. 2401269 3061325317 (Phil Carmody, k=3162)
  83. 2419160 4134666299 (Phil Carmody, k=831)
  84. 2423909 0741237413 (David Broadhurst, k=2)
  85. 2429898 6933122969 (David Broadhurst, k=4)
  86. 2441461 2192680491 (Phil Carmody, k=1955)
  87. 2519705 3454788051 (David Broadhurst, k=25)
  88. 2540651 7061790173 (Phil Carmody, k=714)
  89. 2551771 3686378007 (David Broadhurst, k=1)
  90. 2612774 1634886299 (John Gamble, k=16273)
  91. 2612786 1033132413 (Phil Carmody, k=2146)
  92. 2712025 6264336687 (David Broadhurst, k=61)
  93. 2769936 9354214543 (David Broadhurst, k=89)
  94. 2785079 3614759099 (David Broadhurst, k=1)
  95. 2812471 7603367023 (Patrick Demichel, k=1914391)
  96. 2818647 9203012173 (Phil Carmody, k=294)
  97. 2855619 6279181561 (David Broadhurst, k=20)
  98. 2896194 9050013277 (David Broadhurst, k=22)
  99. 2914600 9705884899 (Phil Carmody, k=2449)
  100. 2981418 0796175099 (Patrick Demichel, k=82949)
  101. 3003964 7115667223 (David Broadhurst, k=1)
  102. 3014988 6408824167 (David Broadhurst, k=1)
  103. 3081017 7651348943 (Patrick Demichel, k=666197)
  104. 3101762 1939478813 (Patrick Demichel, k=556154)
  105. 3133836 2115264623 (David Broadhurst, k=1)
  106. 3144736 3050900739 (David Broadhurst, k=1)
  107. 3151835 5140789859 (Phil Carmody, k=811)
  108. 3188304 0268142317 (Patrick Demichel, k=6766)
  109. 3258660 9914840521 (Phil Carmody, k=140)
  110. 3267846 1339216237 (David Broadhurst, k=2)
  111. 3283993 2584847691 (David Broadhurst, k=5)
  112. 3302026 7984084767 (Patrick Demichel, k=1758841)
  113. 3312114 4337658569 (David Broadhurst, k=4)
  114. 3411764 5273750099 (David Broadhurst, k=51)
  115. 3424305 5459930329 (Phil Carmody, k=188)
  116. 3437569 4455710379 (Phil Carmody, k=831)
  117. 3487524 2850141013 (David Broadhurst, k=2)
  118. 3496999 2067382293 (Patrick Demichel, k=24914)
  119. 3555163 9996444837 (David Broadhurst, k=2)
  120. 3559057 0674147721 (Phil Carmody, k=140)
  121. 3563485 7578246441 (Patrick Demichel, k=1123580)
  122. 3581100 6663085567 (David Broadhurst, k=1)
  123. 3608106 4481860939 (David Broadhurst, k=53)
  124. 3668444 5849990093 (David Broadhurst, k=14)
  125. 3691293 8158377139 (David Broadhurst, k=13)
  126. 3731030 1385064677 (Patrick Demichel, k=217222)
  127. 3767456 3655039499 (David Broadhurst, k=11)
  128. 3812487 1562418943 (David Broadhurst, k=7)
  129. 3816851 3944195357 (John Gamble, k=15462)
  130. 3818131 7989172161 (Phil Carmody, k=160)
  131. 3982004 1998903503 (Phil Carmody, k=119)
  132. 3995473 4529538651 (David Broadhurst, k=25)
  133. 4043446 5014406739 (David Broadhurst, k=1)
  134. 4057975 8072427927 (David Broadhurst, k=1)
  135. 4064029 2130566409 (David Broadhurst, k=28)
  136. 4140698 8181032063 (David Broadhurst, k=29)
  137. 4159769 5930467293 (Norm Dresner, k=12586)
  138. 4174882 6798638601 (David Broadhurst, k=100)
  139. 4178251 0481332717 (Phil Carmody, k=642)
  140. 4199070 9509149567 (David Broadhurst, k=1)
  141. 4239027 7449386437 (Patrick Demichel, k=167182)
  142. 4245664 3750980007 (Patrick Demichel, k=6361)
  143. 4253833 4315325727 (David Broadhurst, k=1)
  144. 4278483 4502256619 (Patrick Demichel, k=51853)
  145. 4283858 4785745733 (David Broadhurst, k=54)
  146. 4283900 6662382767 (David Broadhurst, k=1)
  147. 4306123 3491628837 (Patrick Demichel, k=1055086)
  148. 4320154 9103188771 (Phil Carmody, k=1015)
  149. 4450167 4808177929 (Patrick Demichel, k=317076)
  150. +45445169204709733 (k=9316352850494)
  151. 4600055 6969569687 (David Broadhurst, k=97)
  152. 4751021 9995248979 (Phil Carmody, k=111)
  153. 4757602 4001961681 (Phil Carmody, k=2680)
  154. 4760308 4952523453 (David Broadhurst, k=2)
  155. 4779882 1744153807 (David Broadhurst, k=1)
  156. 4811974 6280879659 (Patrick Demichel, k=2929493)
  157. 4816523 4457776613 (David Broadhurst, k=2)
  158. 4883846 4941565619 (David Broadhurst, k=1)
  159. 4948350 9346945169 (Patrick Demichel, k=484984)
  160. 4963932 4393192087 (David Broadhurst, k=7)
  161. 5217027 5450761583 (David Broadhurst, k=1)
  162. 5255861 0809624609 (Phil Carmody, k=208)
  163. 5376956 7926169037 (David Broadhurst, k=2)
  164. 5440837 8134570329 (David Broadhurst, k=76)
  165. 5478869 0726228449 (David Broadhurst, k=16)
  166. 5557751 3470904287 (David Broadhurst, k=1)
  167. 5657427 5181789961 (Phil Carmody, k=420)
  168. 5703864 7488752899 (David Broadhurst, k=1)
  169. 5706377 7057218929 (Patrick Demichel, k=58648)
  170. 5779596 4049268743 (David Broadhurst, k=11)
  171. 5839170 7876802299 (Phil Carmody, k=3681)
  172. 5863306 8051278887 (David Broadhurst, k=1)
  173. 5930617 7048775259 (Phil Carmody, k=203)
  174. 5934543 2990911099 (David Broadhurst, k=81)
  175. 5947430 3438087011 (Phil Carmody, k=935)
  176. 6089612 7239326823 (David Broadhurst, k=1)
  177. 6100507 7827882687 (David Broadhurst, k=27)
  178. 6129127 0662177557 (Phil Carmody, k=3458)
  179. 6239823 1104871289 (David Broadhurst, k=4)
  180. 6247904 8027493653 (Patrick Demichel, k=197462)
  181. 6251749 5742496299 (Patrick Demichel, k=783671)
  182. 6341112 6340522357 (Paul Leyland, k=33562)
  183. 6364654 4092866703 (Phil Carmody, k=2497)
  184. 6382536 6184273171 (Patrick Demichel, k=164965)
  185. 6434924 4982430407 (Phil Carmody, k=197)
  186. 6536189 4753611413 (Patrick Demichel, k=250114)
  187. 6543329 7088421527 (David Broadhurst, k=1)
  188. 6627712 1590786129 (David Broadhurst, k=8)
  189. 6634564 8882568903 (John Gamble, k=15589)
  190. 6640857 7716936379 (John Gamble, k=15953)
  191. 6761972 8907758477 (David Broadhurst, k=2)
  192. 6934416 7665787849 (Phil Carmody, k=1076)
  193. 7004431 8444113263 (Patrick Demichel, k=2154149)
  194. 7022507 6101446037 (David Broadhurst, k=2)
  195. 7155407 2443048259 (Paul Leyland, k=38003)
  196. 7284714 5154619223 (David Broadhurst, k=1)
  197. 7545001 8210289207 (David Broadhurst, k=1)
  198. 7674926 2490477329 (David Broadhurst, k=8)
  199. 7734579 0367911997 (Patrick Demichel, k=363566)
  200. 7779116 3311930487 (David Broadhurst, k=83)
  201. 7798698 4396557259 (David Broadhurst, k=1)
  202. 7929557 1614568487 (David Broadhurst, k=1)
  203. 7933332 0007933333 (David Broadhurst, k=2)
  204. 7952395 4586701659 (Patrick Demichel, k=1411961)
  205. 8108053 9770489733 (Patrick Demichel, k=42914)
  206. 8115951 6144855853 (David Broadhurst, k=2)
  207. 8415822 5948716477 (Phil Carmody, k=886)
  208. 8435945 6259201379 (David Broadhurst, k=1)
  209. 8538774 4238255167 (Phil Carmody, k=2311)
  210. 8836632 1791014851 (David Broadhurst, k=75)
  211. 8893847 0418382693 (Phil Carmody, k=1994)
  212. 8946624 1197065437 (David Broadhurst, k=2)
  213. 8959689 1585657699 (Phil Carmody, k=223)
  214. 8984963 3324348371 (Patrick Demichel, k=53695)
  215. 9142918 7465604557 (John Gamble, k=17678)
  216. 9157871 8816230383 (David Broadhurst, k=1)
  217. 9167699 9769430087 (Phil Carmody, k=177)
  218. 9349161 6829456477 (Phil Carmody, k=262)
  219. 9509459 6451192601 (David Broadhurst, k=100)
  220. 9627323 9462096659 (David Broadhurst, k=13)
  221. 9641749 3030146619 (David Broadhurst, k=1)
  222. 9697920 0009697921 (Phil Carmody, k=320)
  223. 9857754 1197976567 (David Broadhurst, k=1)
  224. 9985085 4092049611 (David Broadhurst, k=5)

Phil Carmody is organizing a distributed computing project in order to find more factors of Googolplex + 10. If you like these pages I would appreciate that you donate some idle cycles of your computer. You will be cited as the discoverer of the factors you find.